|
ИСТИНА |
Войти в систему Регистрация |
Интеллектуальная Система Тематического Исследования НАукометрических данных |
||
Conformally maximal metrics for Laplace eigenvalues on surfacesстатья
- Авторы: Karpukhin Mikhail, Nadirashvili Nikolai, Penskoi Alexei V., Polterovich Iosif
- Сборник: Surveys in Differential Geometry
- Том: 24
- Год издания: 2019
- Место издания: International Press of Boston
- Первая страница: 205
- Последняя страница: 256
- DOI: 10.4310/sdg.2019.v24.n1.a6
- Аннотация: The paper is concerned with the maximization of Laplace eigenvalues on surfaces of given volume with a Riemannian metric in a fixed conformal class. A significant progress on this problem has been recently achieved by Nadirashvili–Sire and Petrides using related, though different methods. In particular, it was shown that for a given k, the maximum of the k‑th Laplace eigenvalue in a conformal class on a surface is either attained on a metric which is smooth except possibly at a finite number of conical singularities, or it is attained in the limit while a “bubble tree” is formed on a surface. Geometrically, the bubble tree appearing in this setting can be viewed as a union of touching identical round spheres. We present another proof of this statement, developing the approach proposed by the second author and Y. Sire. As a side result, we provide explicit upper bounds on the topological spectrum of surfaces.
- Добавил в систему: Пенской Алексей Викторович